The Framers seemed to have a great affinity for capitalization of sometimes seemingly random words...that does not mean however, that they WEREN'T referring to Vattel's book in the passage you quoted.
Here is a textual transcript of Article I, Section 2 of the Constitution:
The House of Representatives shall be composed of Members chosen every second Year by the People of the several States, and the Electors in each State shall have the Qualifications requisite for Electors of the most numerous Branch of the State Legislature.
No Person shall be a Representative who shall not have attained to the Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.
As I said, they appeared to be big fans of seemingly random capitalization
Requiem æternam dona eis, Domine; In memoria æterna erit justus, ab auditione mala non timebit.
Beauseant!